I wouldn't advise one of those cheap generators. You need an Inverter Generator. I had one of the big cheap ones and had problems with the converter and also keeping batteries charged. I have Yamaha 3000 Inverter now. But we run a 34' Sierra 5th wheel with it. Can't you just plug your camper into the generator? That should charge your battery? Just my $.02

Follow up but not exactly genny related.....
All this talk about battery life and warnings about discharging too far etc...
mostly true but don't forget one of the most important aspects of
keeping your battery(ies) healthy and long lived..... all that time you
aren't using them! All that down time in storage. You need a battery
disconnect switch so your battery isn't being discharged by the sneaky
loads found in every trailer even when you think stuff is all off.
AND GET AND USE A BATTERY TENDER. Keeping your battery 100%
fully charged all the time it's just sitting there "doing nothing" is a biggie.
I got 6 seasons out of my last pair of plain old "marine/crank/deep cycle"
12 volt batteries using a battery tender Jr all the time it's parked.

Check out the PE penalty when your current draw gets in the 20 to 30 amp DC range.

That is why folks that use high draw AC equipment (remember 30 amps @ 12 volts DC is only 360 Watts) like a 1500 watt coffee maker, One battery can not hold the voltage high enough to maintain the inverter's cut out voltage.

Even TWO batteries will be taxed to the max to supply the 125 DC amps required of them.

Having enough battery bank gets expensive the more toys you try to add when on battery.

To the OP...may I suggest a rather backwards approach.....determine your actual use of amp hours...and then buy batteries, chargers and generators that will meet that need.
One way to do this is to buy an essential part of ANY boondocking setup...a battery monitor for about $150 bucks (Victron or Trimetric). This will tell you exactly how many amp hours you are taking out of your battery each day.
Let's say you install one and find you're using 30 amp hours per day. Then you look at your battery and find you have a deep cycle Group 24 battery which CONTAINS when fully charged...75 amp hours...of which you may USE 1/2 without risk of permanently damaging the FUTURE capacity of your battery....or 37.5 amp hours. So...you can't boondock for more than one day on a charged battery. You must either add battery capacity or charging capability or BOTH to stay boondocking.
Lets say you add another battery so you now have 150amp hours of battery and can use 75 of those....giving you a 2+ day camping trip without recharging.
Now...let's say you deplete that 75 amp hours but STILL want to camp some more.
Well...wet cell batteries can take 20-25% of their rating in charging amps...25% of a 150 amp hour bank is 37.5amps...so you don't need more than a 40 amp charger. (TRY IOTA DLS smart series)
A 40 amp charger should be able to put back 75 amps in less than 2 hours...but all batteries slow this process down as they get more "full". Figure 4 hours of charging every 2 days for this set up. A bigger charger WILL NOT change this.

Of course...there's no where to plug in the charger...so you need a generator...but how big a genny? ....Well 40 amps charging at 14.5 volts (bulk) means 580 watts...and since there are losses and inefficiencies in the process, I'd add some decent over capacity...800 watts or so. But you don't need anything more than that to charge THIS battery system. Generators of course are good for other things too...like drills and electric saws and powering big subwoofers!! ;D

Of course you may find that you use way more or way less than 30 amp hours a day when you camp. The above is just an example. A battery monitor not only can help you figure this out...but can then really go to work and let you know where you stand at any moment in time once your system is installed...and will let you know the minute you can turn off that generator once the batts are charged 100%.

David...It is impossible that your wife's CPAP doesn't even use half a volt...because that is NOT what it uses. It uses watts which are amp hours of battery power (@12V nominal) . I assume you mean that your voltmeter readout doesn't even go down .5V during the night. If it does go down .5 volts (STATIC) in a night then your battery or battery bank has lost 50% of its' charge. (12.7V to 12.2 V is 50% used.)
Furthermore...your voltmeter is NOT a battery monitor. It tells you NOTHING about the actual state of your battery IN USE. To know how much battery you have left using THAT meter...you would have to disconnect the battery...wait a minimum of 12 hours and preferably 24 and THEN measure the voltage.

A true battery monitor would solve this problem...but failing that...you should look at the power supply for the CPAP and try to find the watts or amps & volts it uses to determining the ACTUAL total nightly amp hour drain on your batteries. Alternatively...plugging into one of these KILL A WATT meters when home can give you that info...as could a clamp on AMP meter. http://www.amazon.com/P3-P4400-Elect...ill+watt+meter
Several choices.
Since the CPAP is so critical...thought you should be aware of the shortcomings of the voltmeter. At the very least...you'll shorten the life of your batteries relying on one.

Does anyone boondock with a power lift? How much juice would this typically take? I would like to boondock and use my pop up as a glorified tent and wish only to raise and lower the roof. Would I need a genny for this?

Could I just keep the pup plugged into the TV while I do it? Does such a thing work? Would the TV engine generate enough power to send thru the pup to raise the roof?